Balanced Metric and Berezin Quantization on the Siegel-Jacobi Ball

TL;DR

This paper computes key geometric quantities of the Siegel-Jacobi ball, including the balanced metric, scalar curvature, Ricci form, and Laplace-Beltrami operator, and explores Berezin quantization on this manifold.

Contribution

It provides explicit formulas for the balanced metric and related geometric structures on the Siegel-Jacobi ball, advancing understanding of its quantization.

Findings

Explicit matrix of the balanced metric derived

Scalar curvature and Ricci form calculated

Analysis of Berezin quantization on the manifold

Abstract

We determine the matrix of the balanced metric of the Siegel-Jacobi ball and its inverse. We calculate the scalar curvature, the Ricci form and the Laplace-Beltrami operator of this manifold. We discuss several geometric aspects related with Berezin quantization on the Siegel-Jacobi ball.